scholarly journals On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results

2015 ◽  
Vol 368 (9) ◽  
pp. 6539-6574 ◽  
Author(s):  
Henri Johnston ◽  
Andreas Nickel
Keyword(s):  
Tamagawa Number Conjecture ◽  
Tate Motives

scholarly journals The motivic Satake equivalence

2021 ◽  
Author(s):  
Timo Richarz ◽  
Jakob Scholbach
Keyword(s):  
Dual Group ◽  
Tate Motives

AbstractWe refine the geometric Satake equivalence due to Ginzburg, Beilinson–Drinfeld, and Mirković–Vilonen to an equivalence between mixed Tate motives on the double quotient $$L^+ G {\backslash }LG / L^+ G$$ L + G \ L G / L + G and representations of Deligne’s modification of the Langlands dual group $${\widehat{G}}$$ G ^ .

scholarly journals ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE

2017 ◽  
Vol 5 ◽  
Author(s):  
FRANCIS BROWN
Keyword(s):  
Lie Algebra ◽  
Modular Forms ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Explicit Formulae ◽  
Tate Curve ◽  
Tate Motives

This paper draws connections between the double shuffle equations and structure of associators; Hain and Matsumoto’s universal mixed elliptic motives; and the Rankin–Selberg method for modular forms for $\text{SL}_{2}(\mathbb{Z})$. We write down explicit formulae for zeta elements $\unicode[STIX]{x1D70E}_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst–Kreimer conjecture, and solve the double shuffle equations for multiple zeta values in depths two and three.

scholarly journals THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS

2013 ◽  
Vol 56 (2) ◽  
pp. 335-353 ◽  
Author(s):  
PAUL BUCKINGHAM
Keyword(s):  
Number Fields ◽  
Abelian Extension ◽  
Root Number ◽  
Tamagawa Number Conjecture

AbstractFor an abelian extension L/K of number fields, the Equivariant Tamagawa Number Conjecture (ETNC) at s = 0, which is equivalent to the Lifted Root Number Conjecture (LRNC), implies Rubin's Conjecture by work of Burns [3]. We show that, for relative biquadratic extensions L/K satisfying a certain condition on the splitting of places, Rubin's Conjecture in turn implies the ETNC/LRNC. We conclude with some examples.

scholarly journals On Iwasawa theory, zeta elements for 𝔾m, and the equivariant Tamagawa number conjecture

2017 ◽  
Vol 11 (7) ◽  
pp. 1527-1571
Author(s):  
David Burns ◽  
Masato Kurihara ◽  
Takamichi Sano
Keyword(s):  
Iwasawa Theory ◽  
Tamagawa Number Conjecture

On Galois structure invariants associated to Tate motives

1998 ◽  
Vol 120 (6) ◽  
pp. 1343-1397 ◽  
Author(s):  
D Burns ◽  
M Flach
Keyword(s):  
Galois Structure ◽  
Tate Motives

scholarly journals On $p$-adic periods for mixed Tate motives over a number field

2013 ◽  
Vol 20 (5) ◽  
pp. 825-844 ◽  
Author(s):  
Andre Chatzistamatiou ◽  
Sinan Ünver
Keyword(s):  
Number Field ◽  
Tate Motives
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